QGEC : Quantum Golay Code Error Correction

Quantum computers have the possibility of a much reduced calculation load compared with classical computers in specific problems. Quantum error correction (QEC) is vital for handling qubits, which are vulnerable to external noise. In QEC, actual errors are predicted from the results of syndrome measurements by stabilizer generators, in place of making direct measurements of the data qubits. Here, we propose Quantum Golay code Error Correction (QGEC), a QEC method using Golay code, which is an efficient coding method in classical information theory. We investigated our method's ability in decoding calculations with the Transformer. We evaluated the accuracy of the decoder in a code space defined by the generative polynomials with three different weights sets and three noise models with different correlations of bit-flip error and phase-flip error. Furthermore, under a noise model following a discrete uniform distribution, we compared the decoding performance of Transformer decoders with identical architectures trained respectively on Golay and toric codes. The results showed that the noise model with the smaller correlation gave better accuracy, while the weights of the generative polynomials had little effect on the accuracy of the decoder. In addition, they showed that Golay code requiring 23 data qubits and having a code distance of 7 achieved higher decoding accuracy than toric code which requiring 50 data qubits and having a code distance of 5. This suggests that implementing quantum error correction using a Transformer may enable the Golay code to realize fault-tolerant quantum computation more efficiently.